Datasets can be covered by copyright. The threshold of copyright subsisting in material is in the originality and the level of human authorship and demonstrating human creativity in the selection and arrangement of the data.
Machine generated and arranged data (telephone books) fail the test (as proven in case law), at the other end of the scale is data created by human authorship demonstrating human creativity in the selection and arrangement of the data (epidemiological data of health and social status).
Why licence data?
The two sides of the coin of copyright is how you can use others' data, and how others' can use your data. Clear licencing makes it possible for you to use others data, and for them to use yours.
If you aren't sure whether your data is copyright, there is no harm applying a licence which makes the reuse rights clear.
Your funder or journal may stipulate what is required for licencing your data.
Creative Commons (CC)
There are 6 types of Creative Commons licences available to use which cover rights from reuse to modification. They are used widely and understood internationally, and require no registration process aside from applying the logo and text and link to the legally binding licence.
(See poster of licence types, & online tool for licence choice)
*Only CC licences which permit derivative use are suitable for datasets (to enable data to be repurposed)
Creative Commons Zero (CC0)
Not strictly a licence but a rights waiver intended for material for the public domain without need for attribution, thus potentially avoiding' Attribution Stacking'. Be aware though that moral rights are enshrined in Australian law, which include 'right of attribution' of creator/author all content.
Software licences
There are other licences specifically for software: Apache, MIT, GPRL, The Open Software Initiative is a place to begin looking at options.